If you're cutting up a melon for a recipe like the Tomato and Watermelon Salad with Feta from Fine Cooking #118, it's easier to peel it first. But because they're large and round, melons can be awkward to peel. Here's how we like to tackle them:
With a chef's knife, slice oÂťff about 1/2-inch from the ends, enough to expose a circle of flesh. Slice the melon in half crosswise and seed if necessary. Set one of the halves on the large cut side. Slice down the side, following the curve of the melon, deep enough to remove all of the peel without removing the flesh. Cut all the way around, going back to remove any small bits of peel that may remain. Repeat with the other half.